This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The mathematical model consists of the low-frequency Biot's equations in the poroelastic medium and the elastodynamics equation for the elastic one. To realize the coupling, suitable transmission conditions on the interface between the two domains are (weakly) embedded in the formulation. The proposed PolydG discretization in space is then coupled with a dG time integration scheme, resulting in a full space-time dG discretization. We present the stability analysis for both the continuous and the semidiscrete formulations, and we derive error estimates for the semidiscrete formulation in a suitable energy norm. The method is applied to a wide set of numerical test cases to verify the theoretical bounds. Examples of physical interest are also presented to investigate the capability of the proposed method in relevant geophysical scenarios.

翻译：本文研究基于多面体网格的时空有限元间断伽辽金方法（XT-PolydG）在耦合孔隙弹性-弹性介质中波传播数值离散中的分析。数学模型包括孔隙弹性介质中的低频Biot方程和弹性介质的弹性动力学方程。为实现耦合，通过（弱）方式将界面上的合适传输条件嵌入公式中。提出的空间PolydG离散化与时间dG积分方案结合，形成完整的时空dG离散化。我们给出了连续和半离散公式的稳定性分析，并在合适的能量范数下推导了半离散公式的误差估计。该方法应用于广泛的数值测试案例以验证理论界。还展示了具有物理意义的示例，以研究所提方法在相关地球物理场景中的能力。